SOLUTION: How many 5% bags of cement need to be added to 3 bags of 10% cement to make 6%. I thought 12 but I'm not sure how to write the equation. 3 x 10% = 30% + 12 x 5% = 90% / 15 bags

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Question 261212: How many 5% bags of cement need to be added to 3 bags of 10% cement to make 6%. I thought 12 but I'm not sure how to write the equation.
3 x 10% = 30% + 12 x 5% = 90% / 15 bags = 6
Thanks
Found 2 solutions by ankor@dixie-net.com, Theo:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
How many 5% bags of cement need to be added to 3 bags of 10% cement to make 6%
:
5x + 10(3) = 6(x+3)
5x + 30 = 6x + 18
5x - 6x = 18 - 30
-x = -12
x = 12, you are right

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = number of 5% bags.
y = number of 6% bags.

first equation is:

.05*x + .10*3 = .06*y (equation 1)

second equation is:

x + 3 = y (equation 2)

the first equation tells you how the proportion of your mix that is pure cement.

the second equation tells you how many bags of mix.

you need to solve these equations simultaneously.

solve for y in equation 2.

this is already solved as:

y = x + 3

use this value of y in equation 1 to solve for x.

equation 1 is:

.05*x + .10*3 = .06*y

replace y with x + 3 to get:

.05*x + .10*3 = .06*(x+3)

simplify to get:

.05*x + .10*3 = .06*x + .06*3

simplify further to get:

.05*x + .3 = .06*x + .18

subtract .06*x from both sides of this equation and subtract .3 from both sides of this equation to get:

.05*x - .06*x = .18 - .3

simplify to get:

-.01*x = -.12

divide both sides of this equation by -.01 to get:

x = -.12 / -.01 = 12

from equation 2, we get y = x + 3 = 12 + 3 = 15.

we have:

x = 12
y = 15

plug these values into equation 1 to confirm they are good.

equation 1 is .05*x + .10*3 = .06*y

this becomes:

.05*12 + .10*3 = .06*15

simplify to get:

.6 + .3 = .9 which is true confirming our values for x and y are good.

you need to mix 3 bags of 10% cement with 12 bags of 5% cement to get 15 bags of 6% cement.